There are more women on FTSE 350 boards than ever before – 26.1% at FTSE 100 companies and 19.6% at FTSE 250 firms. Davies said 550 women had been appointed in just over four years. There has also been a dramatic reduction in the number of all-male boards. There were 152 in 2011, but there are no all-male boards in the FTSE 100 and only 15 in the FTSE 250, compared with 131 four years ago.

Women on boards: what happens now?

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Davies hailed the “near-revolution which has taken place in the boardroom and profound culture change at the heart of British business”. The former trade minister and chairman of Standard Chartered bank has set a new target of 33% female board members by 2020 and widened the scope to all FTSE 350 firms. But he says the introduction of legally enforced quotas was unwarranted as the progress so far proved that the voluntary approach is working.

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“There is no evidence to warrant an about-turn, but plenty of evidence to show the voluntary regime is working, as each and every month the percentage of women on FTSE boards increases,” the report says.

However, Krystyna Nowak of executive search firm Norman Broadbent, who was at the launch of the report, deplored a “missed opportunity” and said Davies’ recommendations were disappointing. She said many companies would simply continue appointing women to non-executive director positions, leaving the executive board to continue to be dominated by men. She called on the government to address this in its equality-boosting measures planned for 2016.

The UK ranks sixth in Europe behind Norway, Sweden, France, Finland and Belgium, many of which – including Norway, where women make up 35% of board members – have set formal quotas for female representation.

Nora Senior, president of the British Chambers of Commerce, said there was no need for “overbearing government regulation” and called on business to “step up to the task of nurturing the pipeline of women at middle management level on to executive teams”.

The Davies review says “further work and a renewed focus is required” to increase women’s representation further and have more appointed to chair and senior independent director roles. It called for or an independent steering body to be set up to support companies and report next year.

Fiona Woolf, former lord mayor of the City of London, said: “This is no time to rest on our laurels and think the job is done. The figures of 26% of boards now being women of only 100 companies are still far too low when you consider 47% of the workforce and 53% of our graduates are female. The figure of 9.6% in relation to executive positions shows how much room there is for improvement.”

At FTSE 100 companies, consumer goods group Unilever is leading the way after doubling the number of women on its board to 50% since 2011 – the only company to achieve gender parity.

At Marks & Spencer, female board representation has risen to 41.7%, from 27.3% four years ago. Drinks giant Diageo has gone to 40% from 36.4%. At drugmaker AstraZeneca, as well as Sainsbury’s, the proportion of women has risen to 33.3% from 27.3%. British American Tobacco has moved up to 30.8% from 25%; insurer Standard Life has seen a rise to 30% from 27.3%.

The FTSE 100 board with the most dramatic change was Old Mutual, which went from no female representation to 38.5%. Rolls-Royce went from 7.1% to 33.1% while HSBC rose from 16.7% to 42.1%.

Davies called on investors to play a more active role in improving gender balance in companies. He said customers and potential employees should act against companies which do not “get” gender diversity. “I think the customer should not be buying the product from those sorts of companies and young people should not be going to work for them,” he said.

Reacting to the review, the CBI called on the government to assist companies in increasing the representation of women with more free childcare and promoting flexible working.

The Institute of Directors said headhunters and recruiters had a big responsibility to ensure they were looking at candidates from “as wide a pool as possible”. Its chair, Barbara Judge, added: “Women that make it to the top must also help others follow in their footsteps, by acting as role models and mentors.”

New research from Audeliss suggests Britain’s boardrooms risk going into reverse gear over the next 18 months, as the terms of current female non-executive directors expire. The executive search firm warns that because there are too few female executives in the pipeline to replace them, it is likely that the percentage of female non-executive directors on boards will fall from 31% to 26%.